How is the mass of particles in the Large Hadron Collider determined?

[cos]

In his book 'Einstein's Universe' Nigel Calder wrote (16, BBC, 1979) -

"The world's most powerful accelerator of electrons is at Stanford in California...electrons emerge...about 40,000 times 'heavier' than when they started."

Have gamma factors in excess of that amount been generated?

How is the relativistic mass of an accelerated particle determined?

I read somewhere that the mass of a particle accelerated in a cyclotron is determined in accordance with the amount of energy that has to be applied laterally to the particle in order to maintain its circular trajectory but what is the process in relation to straight-line acceleration?

 

[jtbell]

Have gamma factors in excess of that amount been generated?

More powerful accelerators have been built since Calder wrote his book. The Large Electron Positron (LEP) collider at CERN accelerated electrons and positrons to 209 GeV energy, which corresponds to a Lorentz gamma factor of about 409000.

How is the relativistic mass of an accelerated particle determined?

Calder probably simply used the usual equation $E = m_{relatvistic} c^2$.

Particle physicists (the people who actually use these accelerators) don't use the concept of relativistic mass, or measure it. They always use the invariant mass (a.k.a. "rest mass") and use corresponding equations to calculate energy and momentum:

$$E = \gamma m c^2 = \frac{mc^2}{\sqrt{1 - v^2 / c^2}}$$

$$p = \gamma m v = \frac {mv}{\sqrt{1 - v^2 / c^2}}$$

Actually, they use their detectors to measure the energy and momentum by various means. One way to identify a particle is to measure E and p independently, then calculate the (invariant) mass using $mc^2 = \sqrt{E^2 - (pc)^2}$. Or, if they can identify the particle by other means (by the characteristics of its interactions), and thereby know m, they can measure E and then calculate p, or measure p and then calculate E. It all depends on the particular experiment and the kinds of detectors that it uses.

To the physicists working on experiments at LEP, the circulating electrons and positrons had a mass of 511 keV/c^2, same as when at rest, an energy of 209 GeV, and a momentum of 209 GeV/c minus a tiny smidgen.

 

[cos]

More powerful accelerators have been built since Calder wrote his book. The Large Electron Positron (LEP) collider at CERN accelerated electrons and positrons to 209 GeV energy, which corresponds to a Lorentz gamma factor of about 409000.

Much appreciated.

 

[cos]

I recently read an article stating that 'if an electron was boosted to 10^40 its rest mass it would have an energy of 5.11x10^39Mev which is beyond the range of the LHC.'

What is 'the range of the LHC'?

 

[jtbell]

http://www.google.com/search?q=lhc

 

[cos]

http://www.google.com/search?q=lhc

Thanks for that reference; I emailed Gareth James who informed me "the energy of the LHC is 7 TeV (7x10^12 eV)."

 

[cam875]

"The Large Hadron Collider (LHC) is the world's largest and highest-energy particle accelerator, intended to collide opposing particle beams, of either protons at an energy of 7 TeV/particle, or lead nuclei at an energy of 574 TeV/nucleus." first paragraph on the wiki, no need to have emailed someone lol.